Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): At a certain point, two plane electromagnetic waves have their electric fields in opposite directions and their magnetic fields in the same direction. The two waves are travelling in opposite directions.
Reason (R): An electromagnetic wave travels along the direction of \( \vec{E}\times\vec{B} \).
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both (A) and (R) are true and (R) is the correct explanation of (A).
Assertion (A) At a certain point, two plane electromagnetic waves have their electric fields in opposite directions and their magnetic fields in the same direction. The two waves are travelling in opposite directions. — True. Take the first wave with \( \vec{E} \) along \( +\hat{\jmath} \) and \( \vec{B} \) along \( +\hat{k} \). It travels along \( \hat{\jmath}\times\hat{k}=+\hat{\imath} \). The second wave has \( \vec{E} \) along \( -\hat{\jmath} \) and the same \( \vec{B} \), so it travels along \( (-\hat{\jmath})\times\hat{k}=-\hat{\imath} \).
Reason (R) An electromagnetic wave travels along the direction of \( \vec{E}\times\vec{B} \). — True. \( \vec{E} \) and \( \vec{B} \) are perpendicular to each other and to the direction of propagation. Their cross product points in the direction in which the wave moves.
Why R explains A?
Reversing one factor of a cross product reverses the product, so \( (-\vec{E})\times\vec{B}=-(\vec{E}\times\vec{B}) \).
Since the direction of travel is the direction of \( \vec{E}\times\vec{B} \), the second wave must move opposite to the first. So (R) is the correct explanation of (A).
NCERT (2026-27):
Example 8.1 – “To find the direction, we note that E is along y-direction and the wave propagates along x-axis. Therefore, B should be in a direction perpendicular to both x- and y-axes. Using vector algebra, E × B should be along x-direction.”